Constant Focal Length Research Articles

Dynamic polarization-regulated metasurface with variable focal length

Polarization and focal length are both critical optical parameters with many applications in many fields, such as optical communications and imaging. The development of metasurfaces provides a new realization of optical systems. In this paper, based on metasurfaces’ powerful electromagnetic modulation capability, we integrate polarization conversion with continuous zoom function and propose a dynamic polarization-regulated metasurface with variable focal length. It realizes the reversible conversion of polarization state, which can convert linearly polarized light into elliptically polarized light and circularly polarized light and convert circularly polarized light to linearly polarized light. At the same time, it achieves a 4.4× zoom range, with a constant focal length variation from 70 µm to 309 µm. The metasurface has the advantages of small size, easy integration, and reconfigurability, providing a new design idea for complex functional optical systems.

Curved retina-like camera array imaging system with adjustable super-resolution fovea

To achieve non-uniform imaging with a large field of view and high efficiency as well as to obtain an adjustable fovea with super-resolution, we proposed a curved retina-like camera array imaging system (CRCS), which is built by an eight-camera array distributed non-uniformly on a curved surface and a camera coaxial with Risley prisms located in the center. By the non-uniform imaging, the field of view of the developed prototype is 150∘×40∘ with a reduction of data redundancy by 87.62%. Besides, the experimental results show that CRCS can obtain clear and sharp images of farther targets of interest around the fovea field of view with a constant focal length.

The Influence of Autofocus Lenses in the Camera Calibration Process

Camera calibration is a crucial step in robotics and computer vision. Accurate camera parameters are necessary to achieve robust applications. Nowadays, camera calibration process consists of adjusting a set of data to a pin-hole model, assuming that with a reprojection error close to zero, camera parameters are correct. Since all camera parameters are unknown, computed results are considered true. However, the pin-hole model does not represent the camera behavior accurately if the autofocus is considered. Real cameras with autofocus lenses change the focal length slightly to obtain sharp objects in the image, and this feature skews the calibration result if a unique pin-hole model is computed with a constant focal length. In this article, a deep analysis of the camera calibration process is done to detect and strengthen its weaknesses when autofocus lenses are used. To demonstrate that significant errors exist in computed extrinsic parameters, the camera is mounted in a robot arm to know true extrinsic camera parameters with an accuracy under 1 mm. It is also demonstrated that errors in extrinsic camera parameters are compensated with bias in intrinsic camera parameters. Since significant errors exist with autofocus lenses, a modification of the widely accepted camera calibration method using images of a planar template is presented. A pin-hole model with distance-dependent focal length is proposed to improve the calibration process substantially.

Paraxial design of a four-component zoom lens with zero separation of principal planes and fixed position of an image focal point composed of members with constant focal length.

Our paper presents a detailed theoretical analysis of a four-component zoom lens with coincident principal planes, fixed position of the image focal point, and an approximately corrected Petzval sum. New formulas enabling the calculation of paraxial parameters of such optical systems are derived, and the practical application of these formulas is shown in an example. The position of the optical center of these optical systems does not depend on the object distance (for a given value of focal length of the zoom), and the position of the image focal point (with respect to the last element of the system) is fixed during the operation of the zoom. Such optical systems could be used in various measuring systems in photogrammetry, computer vision, triangulation sensors, fringe projection techniques, surveying, machine vision, etc.

Generation of propagation-invariant and intensity-controlled dark hollow beams by a refractive beam shaping system.

Dark hollow beams (DHBs) have great potential in the applications of optical manipulation, and the generation of DHBs is still a challenging and rewarding issue. In this paper, we present a beam shaping system for generating DHBs. The proposed system is composed of a freeform lens array and a non-classical zoom system which has a constant focal length but various image locations. The DHBs with a well-controlled intensity profile generated by the proposed system is not sensitive to the change of the intensity distribution of the incident beam, which allows flexible choices of light sources. Moreover, the annular pattern produced by the DHB remains unchanged when the image plane is moved a long distance of 17mm, and the energy efficiency of the beam shaping system is greater than 90% when Fresnel loss is considered. The proposed beam shaping system endows the generated DHBs with new properties and may have great potential in the field of optical tweezers and atom guides.

Calibration method for a structured light measurement system with two different focal length cameras

During reconstructing objects with complex shapes, 3D object surfaces are anticipated with an elaborate description to surface features and a fast acquiring speed. While a Camera–Projector Structured Light (CPSL) system with a constant focal length cannot achieve the two goals. The CPSL system with a Long Focal Length (LFL) camera has a high resolution and a small measurement area, therefore, high sampling density and low measurement efficiency. Conversely, the system with a Short Focal Length (SFL) camera has high measuring efficiency without enough sampling density. To accomplish the two goals, we propose a novel system integrating with two types of CPSL system. One system with the SFL camera fast obtains the overall morphology of objects. Another with the LFL camera acquires the details of surface features very well. To integrate them, a novel calibration method is presented. Experimental results verify the robustness and accuracy of the proposed calibration method.

Dispersion tuning with a varifocal diffractive-refractive hybrid lens

We present a hybrid diffractive-refractive optical lens doublet consisting of a varifocal Moiré Fresnel lens and a polymer lens of tunable refractive power. The wide range of focal tunability of each lens and the opposite dispersive characteristics of the diffractive and the refractive element are exploited to obtain an optical system where both the Abbe number and the refractive power can be changed separately. We investigate the performance of the proposed hybrid lens at zero overall refractive power by tuning the Abbe number of a complementary standard lens while maintaining a constant overall focal length for the central wavelength. As an application example, the hybrid lens is used to tune to an optimal operating regime for quantitative phase microscopy based on a two-color transport of intensity (TIE) approach which utilizes chromatic aberrations rather than intensity recordings at several planes to reconstruct the optical path length of a phase object.

Efficient Video Rectification and Stabilisation for Cell-Phones

This article presents a method for rectifying and stabilising video from cell-phones with rolling shutter (RS) cameras. Due to size constraints, cell-phone cameras have constant, or near constant focal length, making them an ideal application for calibrated projective geometry. In contrast to previous RS rectification attempts that model distortions in the image plane, we model the 3D rotation of the camera. We parameterise the camera rotation as a continuous curve, with knots distributed across a short frame interval. Curve parameters are found using non-linear least squares over inter-frame correspondences from a KLT tracker. By smoothing a sequence of reference rotations from the estimated curve, we can at a small extra cost, obtain a high-quality image stabilisation. Using synthetic RS sequences with associated ground-truth, we demonstrate that our rectification improves over two other methods. We also compare our video stabilisation with the methods in iMovie and Deshaker.

Spreading of a charged microdroplet

We consider the spreading of a charged conducting droplet on a flat dielectric surface. Two forces drive the spreading: surface tension and electrostatic repulsion. By using the lubrication approximation we derive a fourth order nonlinear partial differential equation that describes the evolution of the height profile. We find that the equation has a two-parameter family of selfsimilar solutions. Some of the solutions are explicitly computed while the other solutions are studied numerically. We show that the solutions have moving contact lines and the radius of the drop is a power law of time with exponent one-tenth. We also construct explicit solutions corresponding to non-circular drops, whose interfaces are ellipses with constant focal length.

Asymmetric fan-beam configurations with spatially varying focal lengths and shift-variant filtering reconstruction

We present an algorithm for image reconstruction from data acquired by use of an asymmetric fan-beam configuration with a spatially varying focal length. This algorithm is a natural generalization of our previous algorithm for fan-beam computed tomography (CT) that involves shift-variant filtering, and it possesses desirable noise and numerical properties similar to those in the previous algorithm. We performed computer simulation studies to validate and evaluate the proposed algorithm, and quantitative results demonstrate that the proposed algorithm possesses desirable noise and numerical properties. The filtered backprojection algorithm can reconstruct images from data acquired in a configuration with a constant focal length. In this situation, the proposed algorithm yields images with lower and more uniform noise properties than the filtered backprojection algorithm.

A parabolic mirror x-ray collimator

A robust and stable x-ray collimator has been developed to produce a parallel beam of x-rays by total external reflection from a parabolic mirror. The width of the gold-coated silica mirror varies along its length, which allows it to be bent from a plane surface into a parabolic form by application of unequal bending forces at its ends. A family of parabolas of near constant focal length can be formed by changing the screw-applied bending force, thus allowing the collimator to cater for a range of wavelengths by the turning of a screw. Even with radiation with a wavelength as short as that as Mo K1 ( = 0.07 nm), a gain in flux by a factor of 5.5 was achieved. The potential gain increases with wavelength, e.g. for Cu K1 radiation this amounts to over a factor of ten.

Nickel-titanium versus stainless-steel finger spreaders in curved canals

Placement of endodontic spreaders to within 1 to 2 mm of the root canal working length has been advocated for optimum gutta-percha obturation. Due to their stiffness, stainless-steel (SS) spreaders will often fail to achieve this position in curved canals. Newly marketed nickel-titanium (NiTi) spreaders may offer an advantage in this regard due to the increased flexibility of these instruments. Seventy mesial and distal mandibular molar canals were instrumented to a #35 master apical file size. Measurements of the canal curvature were made from preoperative radiographs. Canal curvature angles ranged from 0 to 51 degrees. The teeth were placed in a radiographic mount to ensure a constant focal length, and postoperative radiographs were exposed with comparably sized SS and NiTi spreaders inserted into each prepared canal. Measurements of spreader tip to apex distance were made with a micrometer to the nearest 0.02 mm on the radiographs. Using a t test for paired samples, it was shown that NiTi spreaders penetrated to a significantly greater depth than SS spreaders in curved canals (p < 0.001).

The interaction between excimer laser energy and vascular tissue

The effects of XeF1 excimer laser on isolated normal and atherosclerotic aorta were studied. Experiments were performed in flowing water at constant temperature, flow rate, water depth, pulse width (10 nsec), wavelength (351 nm), beam size (1 mm 2) and focal length (50 cm). The number of pulses, the pulse energy, and the pulse frequency were varied, and the vascular tissue was studied histologically. The following observations were made: (1) tissue ablation required a minimum threshold pulse energy and was nonlinearly proportional to the number of pulses and the pulse energy delivered; (2) precise tissue ablation occurred at low pulse frequencies, but changes resembling a thermal process were seen as pulse frequency increased; (3) calcified plaque was more photoresistant than atheroma or normal vessel; (4) excimer laser energy was markedly attenuated by blood; and (5) the time interval between pulses and high peak power are related to the precision of ablation by pulsed excimer laser. It is concluded that excimer laser can rapidly and precisely ablate vascular tissue by a photothermal process.

Focusing properties of solid ultrasonic cylindrical lenses

The sound velocity, thermal coefficient of sound velocity, and attenuation coefficients of 20 common plastics were measured and used as a basis for the design of several lenses. Materials selected were polyethylene, nylon, polystyrene, polyphenylene oxide, and a low-sound-velocity silicone rubber compound. Using common geometrical optical techniques, lenses were designed to minimize off-axis aberrations for focal-length-to-aperture ratios ranging from 1 to 3 and aperture-to-wavelength ratios up to 150. Using methods analogous to chromatic aberration correction in optics, lenses were designed for constant focal length over a temperature range of 0° to 30°C. Two- and four-element lens systems with apertures up to 30 cm were fabricated from the selected materials. Measurements were made in the frequency range 600 kHz to 1.2 MHz and good agreement with theoretical predictions of focal length and directional response was observed. The effects of shear waves were not evident. The theoretical model used to evaluate lens performance was based on the numerical evaluation of the Fresnel-Kirchhoff diffraction integral. This work shows that it is possible, using established optical design methods and commonly available solid materials, to fabricate athermal acoustic lenses with good performance characteristics at aperture-to-wavelength ratios up to 150.

Focusing Properties of Solid Multielement Acoustic Lenses

The sound velocity, thermal coeffecient of sound velocity, and attenuation coefficients of 20 common plastics were measured and used as a basis for the design of several lenses. Materials selected were polyethylene, nylon, polystyrene, polyphenylene oxide, and a low sound velocity silicone rubber compound. Using common geometrical optics techniques, lenses were designed to minimize off-axis aberrations for focal length to aperture ratios ranging from 1 to 3 and aperture-to-wavelength ratios up to 150. Using methods analogous to chromatic aberration correction in optics, lenses were designed for constant focal length over the temperature range 0–30°C. Two and four element lens systems with apertures up to 30 cm were fabricated from the selected materials. Measurements were made in the frequency range 300 kHz–1.2 MHz, and good agreement with theoretical predictions of focal length and directional response was observed. The effects of shear waves were not evident. The theoretical model used to evaluate lens performance was based on the numerical evaluation of the Fresnel-Kirchhoff diffraction integral. This work shows that it is possible, using established optical design methods and commonly available solid materials, to fabricate athermal acoustic lenses with good performance characteristics at aperture-to-wavelength ratios up to 150.